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IRT (item response theory)

Explore the relationship between unobserved latent characteristics such as mathematical aptitude and the probability of correctly answering test questions (items). Or explore the relationship between unobserved health and self-reported responses to questions about mobility, independence, and other health-affected activities. IRT can be used to create measures of such unobserved traits or place individuals on a scale measuring the trait. It can also be used to select the best items for measuring a latent trait. IRT models are available for binary, graded, rated, partial-credit, and nominal response items. Visualize the relationships using item characteristic curves, and measure overall test performance using test information functions. And much more.

Learn about IRT (item response theory).

Binary response models

  • One-parameter logistic (1PL)
  • Two-parameter logistic (2PL)
  • Three-parameter logistic (3PL)

Ordinal response models

  • Graded response
  • Partial credit
  • Generalized partial credit
  • Rating scale

Categorical response model

  • Nominal response

Hybrid models with differing response types

Multiple-group IRT models

  • Allow parameters to vary across groups
  • Constrain parameters across groups to be equal
  • Available for all IRT models
  • Test for differences across groups


  • Item characteristic curves and boundary characteristic curves
    • Plot midpoint probabilities
  • Category characteristic curves
  • Test characteristic curve
    • Plot expected score for a specified ability level
    • Plot ability for a specified expected score
  • Item information functions
  • Test information function
    • Plot the standard error
  • Fully customizable graphs
  • Save your graphed results as datasets for future use

DIF diagnostics

  • Mantel–Haenszel test
  • Logistic regression test
  • IRT model-based test

Control panel interface

  • Access all IRT features
  • Easily select response type and item variables
  • Even create hybrid models
  • Estimate models
  • Select and customize graphs
  • Manage reporting of results

Control how your output is displayed

  • Sort by difficulty
  • Sort by discrimination
  • Group estimates by type or by item
  • Show results only for selected items
  • Compare IRT estimates across groups

Postestimation Selector

  • View and run all postestimation features for your command
  • Automatically updated as estimation commands are run

Additional resources

See New in Stata 18 to learn about what was added in Stata 18.